Should the Golden Ratio Be Used in Industrial Design?

Max is not ready to change the layout of his BIGASS Display quite yet, but he's not ruling it out either.

You probably won’t be too surprised to hear that this column relates to my ongoing Bodacious Acoustic Diagnostic Astoundingly Superior Spectromatic (BADASS) Display project. As you may recall, this little beauty is going to boast a 16 x 16 array of tricolored LEDs. In my previous blog on this project, in which we discussed the physical implementation and presentation, I noted that I had spaced out the LEDs more on the horizontal axis than on the vertical axis so as to increase the visual appeal of the display.

My vertical spacing between pixels is 33.33mm. This spacing is fixed because I'm using NeoPixel Strips from Adafruit -- the type with 30 NeoPixels per meter -- with the LEDs controlled by an Arduino Mega boasting an Atmel microcontroller. For my display, I decided to use a multiplication factor of 1.5, thereby giving me a horizontal spacing of 33.33mm * 1.5 ≈ 50mm.

In the comments to that blog, EETimes member Perl_Geek made the following suggestion:

You might want to consider employing the Golden Ratio (1.618:1 -- close enough for government work) in your rectangular layout. Doing so several times would be even cooler.

Hmm, that's certainly something to think about. In mathematics, two quantities are said to be in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. This is much easier to visualize graphically (well, it would be, wouldn’t it?) as illustrated below:

On the left we see a "golden line," while a "golden rectangle" is shown on the right. If we do the math, as illustrated below, we discover that the golden ratio works out at ≈1.618.

The golden ratio pops up all over the place in nature. For example, it is expressed in the arrangement of branches along the stems of plants, the branching on veins and nerves in animals, the proportions of chemicals in compounds, the geometry of crystals, and… the list goes on.

Many people seem to find things in proportion to the golden radio to be aesthetically pleasing. Based on this, some artists and architects have created their works so as to reflect this proportion (many of the proportions of the Parthenon on Greece are said to exhibit the golden ratio, for example).

Now, I was aware of the golden ratio (What engineer isn’t?), but I've never actually heard about it being employed in industrial design, so I decided to perform a simple experiment. Remember that each of my LEDs is going to be accompanied by a 20mm-diameter brass washer. First, I created an array in which the horizontal and vertical separations between elements were both 33.33mm as illustrated below:

Horizontal separation = 1.0x vertical separation. (Click here to see a full-sized version that you can print out and experiment with yourself.)

Next, I made the horizontal spacing 1.5X the vertical spacing (the way I currently have things set up on the BIGASS Display), that is, 33.33mm * 1.5 ≈ 50mm as illustrated below:

Horizontal separation = 1.5x vertical separation. (Click here to see a full-size version that you can print out and experiment with yourself.)

Finally, I related the horizontal spacing to the vertical spacing using the golden ratio, that is, 33.33mm * 1.618 ≈ 54mm as illustrated below:

Horizontal separation = 1.6x vertical separation. (Click here to see a full-sized version that you can print out and experiment with yourself.)

I then went for a wander around the building to see what people thought. Well, wouldn’t you know it? Almost everyone had gone out for lunch! Happily, I did manage to track down two engineers. I talked to them independently and I didn’t mention anything about golden radios. Just to give them some reference to work from, however, I did explain that this was to be an array of LEDs presenting the spectral information from an audio stream, with the amplitude of the various frequency elements being presented on the vertical axis.

One of the engineers said he preferred the first pattern -- the one with equal horizontal and vertical spacing -- on the basis that one could present more information in a smaller area. Well, that certainly makes sense in an engineering-over-aesthetics sort of way. Interestingly enough, the other engineer said he preferred to have a wider horizontal spacing for visual interest. Furthermore, after glancing back and forth for a while, he said that -- although he couldn’t explain why -- he was more drawn to the last example (the one employing the golden ratio).

The difference between my 1.5 ratio and the golden ratio, which resulted in horizontal separations of 50mm and 54mm, respectively, is only 4mm, but that was enough to persuade this engineer to prefer the golden ratio.

Of course, a sample of two people is statistically meaningless, but it does make you think. I'm not ready to change the layout of my BIGASS Display quite yet (since the thought of re-laying out all 256 LEDs brings tears to my eyes), but I'm not ruling it out either.

As I mentioned earlier, I've never actually heard about the golden ratio being employed in industrial design -- have you? Also, if you have the time, it would be great if you could click the links above, print out the larger versions of my images, perform your own survey amongst your coworkers, and then report your findings back here. Based on these results, I will decide if a change in direction is on the cards for my BIGASS display.

If you take some measurements of important areas of the palm of your hand, you will find something interesting. Take the distance from the "large" knuckle of your index finger to the inner point where your thumb "diverges" from the rest of your hand. This is line A. Take the distance, again from said knuckle of the index finger, to the equivalent knuckle of the pinky finger. This is line B. The ratio B:A is awfully close to Phi (properly known as the golden section). I deliberately chose these proportions for comfortable "hand appeal" with a project oof mine, the BLiVIT.

Engineers typically being horrible aesthetic designers - myself included - it is useful to default back to that ratio whenever there is an arbitrary question of style involved - it is hiding in plain sight within everything I have designed over the past 30 years.

I have never found it to give any particular performance benefit in optical designs, but I did once develop an optical reflector optimization technique that used genetic algorithms to perfect reflective surfaces that consistently spat out Nautilus shells in preference to the expected parabolas.

"Hiding in the design" is the spirit in which many of its practitioners have used it over the past few thousand years anyway. A nod to other educated people viewing the work. Worst-case using it makes me feel like I stand shoulder to shoulder with the likes of Vitruvius, Medieval Cathedral Masons and Leonardo for a few modern moments. The idea of some universal truth hidden in a cell phone housing that the Renaissance masters would "get" is rather appealing to me. We all like inside jokes.

Again, I only use the ratio myself when no other criteria drives a particular dimensional selection, but I definitely do enjoy getting to use it when I can - in fact I have it on speed-dial in my Pro/Engineer and Altium seats here. The best aesthetic designers I know definitely don't use it on a regular basis. I recall using it as a driving ratio for surface development in molded plastic housings on one particular project and it did not look good at all. There is excellent debunking content around the subject on the Skeptoid site btw. I believe the number actually has its own Fbook page too - or did a few years back anyway.

In a world where the bulk of the work of the readers here is thrown into the recycling bin just a few years after they complete it, it feels nice to at least for a while stand alongside cathedrals that have lasted a thousand years. Unfortunately most of the time today if one's engineering decisions are not immediately driven by regulatory code, cost and compelling structural and mechanical fit reasons then the chances are you are missing something important from the design brief in the first place. Around 50% of those medieval cathedral towers fell down on the first go-around remember.

Even today in modern physics many believe there is a strange harmonic numeric relationship between the fundamental constants of the universe, so maybe there is something special about numbers after all – we just haven't found what it is yet. God may well be man writ large, but he or she probably looks nothing like a giant cell phone.

@Disquisitioner: One thing to keep in mind before you decide whether to use the Golden Ratio is to look at it in terms of overall display size as well as the spacing between the elements.

I agree -- thsi is the sort of thing that has a ripple-on effect -- it's not sufficient to pick a rule and use if for just one element of the display -- you have to keep everything in harmony -- my mind is still churning with thoughts on all of this...

One thing to keep in mind before you decide whether to use the Golden Ratio is to look at it in terms of overall display size as well as the spacing between the elements. All the samples in your blog post are either 3x4 or 5x6, so even though you have the Golden Ratio spacing of 1.6x between the individual elements that overall size of the samples as a unit doesn't reflect the Golden Ratio. Try a test where you print out a sample that is NxN and uses a spacing of 1.6x between the individual elements (horizontal and vertical). Then not only would the Golden Rule be reflected in element spacing but in the overall display.

Your BADASS Display will be 16x16 when finished so if you do use the Golden Ratio as the spacing factor then it will be not only 1.6x between elements but 1.6x horizontal vs. vertical in the total display. That might heighten the visual impact (positively, I suspect) of the Golden Ratio.

I don't know whether this will influence your opinion or that of your test subjects, but I'd make that part of the test just to be sure before you decide.

Just because someone called it the golden ratio, doesn't mean it's ever really used. In fact it's very conspicuous by its absence in the standards of the modern world.

If you examine the aspect ratio of painting canvases, film sizes, standard photographic paper, screen sizes or paper sizes, you will find that none of them follow the golden rule. In fact there is no consistency whatsoever in aspect ratios in the modern world. They plot all over the graph.

If you frame a picture perfectly in your camera, no matter what the film or sensor size, there often isn't a single standard paper size that will fit the same aspect ratio. In fact photographic paper sizes are all over the map as you increment sizes. Even the 4K standard is a different aspect ratio than Ultra HD. 2K is different from HD. Movie screen aspect ratios are also quite varied. When you think about it, it's quite stupid, like incompetent CEOs on power trips.

Most HD Camcorder's viewfinders show a cropped version of what's recorded, so your HDTV shows more than you bargained for. What's wrong with those designers?

I sometimes wonder why most artists restrict their artistic freedom by fitting their paintings to a specific arbitrary canvas size. I often trim my photographic prints to the aspect ratio that fits the scene.

American standard paper sizes such as A at 8.5" x 11" = 1.294, while doubling to B at 11 x 17 = 1.545 isn't even close. The European standard aspect ratio for paper makes the most sense as it is fixed at 1.414, so doubling maintains the same aspect ratio, so every European paper size has the same aspect ratio. They don't have the misfit problem when they shrink a print by one size.

So I wouldn't worry too much about your project not meeting the "golden rule". Let's just say it met your platinum rule. It's called artistic license, so take advantage of it.